alphaBB

alphaBB: A Global Optimization Method for General Constrained Nonconvex Problems. A branch and bound global optimization method, ffBB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convexrelaxation of the original nonconvexproblem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bilinear, fractional, signomial) with customized tight convex lower bounding functions and (ii) by utilizing the ff parameter as defined in [17] to underestimate nonconvex terms of generic structure. The proposed branch and bound type algorithm attains finite ffl--convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems. The global optimization method, ffBB, is implemented in C and tested on a variety of example problems.


References in zbMATH (referenced in 49 articles )

Showing results 1 to 20 of 49.
Sorted by year (citations)

1 2 3 next

  1. Dalkiran, Evrim; Sherali, Hanif D.: RLT-POS: reformulation-linearization technique-based optimization software for solving polynomial programming problems (2016)
  2. Lee, Yu-Ching; Pang, Jong-Shi; Mitchell, John E.: An algorithm for global solution to bi-parametric linear complementarity constrained linear programs (2015)
  3. Lundell, Andreas; Skjäl, Anders; Westerlund, Tapio: A reformulation framework for global optimization (2013)
  4. Teles, João P.; Castro, Pedro M.; Matos, Henrique A.: Multi-parametric disaggregation technique for global optimization of polynomial programming problems (2013)
  5. Bompadre, Agustín; Mitsos, Alexander: Convergence rate of McCormick relaxations (2012)
  6. Misener, Ruth; Floudas, Christodoulos A.: Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations (2012)
  7. Price, C.J.; Reale, M.; Robertson, B.L.: A cover partitioning method for bound constrained global optimization (2012)
  8. Birgin, E.G.; Bueno, L.F.; Krejić, N.; Martínez, J.M.: Low order-value approach for solving var-constrained optimization problems (2011)
  9. Domes, Ferenc; Neumaier, Arnold: Rigorous enclosures of ellipsoids and directed Cholesky factorizations (2011)
  10. Wu, Dan; Shang, Youlin: Complete solutions to general box-constrained global optimization problems (2011)
  11. Shao, Junwei; Hou, Xiaorong: Positive definiteness of Hermitian interval matrices (2010)
  12. Stein, O.; Winterfeld, A.: Feasible method for generalized semi-infinite programming (2010)
  13. Ho, Yuen-Hong Alvin; Kwan, Hing-Kit; Wong, Ngai; Ho, Ka-Leung: Designing globally optimal delta-sigma modulator topologies via signomial programming (2009)
  14. Liberti, Leo: Reformulations in mathematical programming: Definitions and systematics (2009)
  15. Chen, Xi; Yang, Jing; Li, Zhaohua; Tian, Daqing; Shao, Zhijiang: A combined global and local search method to deal with constrained optimization for continuous tabu search (2008)
  16. Dhyani, Kanika; Liberti, Leo: Mathematical programming formulations for the bottleneck hyperplane clustering problem (2008)
  17. Gounaris, Chrysanthos E.; Floudas, Christodoulos A.: Tight convex underestimators for $\mathcal C^2$-continuous problems. I: Univariate functions (2008)
  18. Jach, Matthias; Michaels, Dennis; Weismantel, Robert: The convex envelope of $(n-1)$-convex functions (2008)
  19. Nowak, Ivo; Vigerske, Stefan: Lago: a (heuristic) branch and cut algorithm for nonconvex minlps (2008)
  20. Floudas, Christodoulos A.; Kreinovich, Vladik: Towards optimal techniques for solving global optimization problems: symmetry-based approach (2007)

1 2 3 next